Measure and Integration - Bercovici, Hari.; Brown, Arlen; Pearcy, Carl.; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2016)
This book covers the material of a one year course in real analysis. It includes an original axiomatic approach to Lebesgue integration which the authors have found to be effective in the classroom. Each chapter contains numerous examples and an extensive problem set which expands considerably the breadth of the material covered in the text. Hints are included for some of the more difficult problems. .
Rings of sets -- Measurability -- Integrals and Measures -- Convergence Theorems for Lebesgue Integrals -- Existence and Uniqueness of Measures -- Signed Measures, Complex Measures and Absolute Continuity -- Measure and Topology -- Product Measures -- The Lp Spaces -- Fourier Analysis -- Standard Measure Spaces. .
Keywords: Mathematics; Measure theory; Functions of real variables; Mathematics; Measure and Integration; Real Functions; Electronic books